Study Guide and Intervention (continued) - MathnMind

6-1
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Study Guide and Intervention
Solving Inequalities by Addition and Subtraction
Solve Inequalities by Addition Addition can be used to solve inequalities. If any
number is added to each side of a true inequality, the resulting inequality is also true.
Addition Property of Inequalities
For all numbers a, b, and c, if a b, then a c b c,
and if a b, then a c b c.
The property is also true when and are replaced with and .
Example 1 Example 2
Solve x 8 6. Then graph it on a number line.
x 8 6 Original inequality
x 8 8 6 8 Add 8 to each side.
x 2 Simplify.
The solution in set-builder notation is
{x|x 2}.
Number line graph:
4 3 2 1 0 1 2 3 4
Exercises
Solve 4 2a a. Then
graph it on a number line.
4 2a a Original inequality
4 2a 2a a 2a Add 2a to each side.
4 a Simplify.
a 4 4 a is the same as a 4.
The solution in set-builder notation is {a|a 4}.
Number line graph:
2 1 0 1 2 3 4 5 6
Solve each inequality. Then check your solution, and graph it on a number line.
1. t 12 16 2. n 12 6 3. 6 g 3
26 27 28 29 30 31 32 33 34
4. n 8 13 5. 12 12 y 6. 6 s 8
10 9 8 7 6 5 4 3 2
Solve each inequality. Then check your solution.
7. 3x 8 4x 8. 0.6n 12 0.4n 9. 8k 12 9k
1 4
10. y 10 15 2y 11. z 12. 2b 4 3b
3 3
Define a variable, write an inequality, and solve each problem. Then check your
solution.
13. A number decreased by 4 is less than 14.
12 13 14 15 16 17 18 19 20
4 3 2 1 0 1 2 3 4
14. The difference of two numbers is more than 12, and one of the numbers is 3.
15. Forty is no greater than the difference of a number and 2.
7 8 9 10 11 12 13 14 15
4 3 2 1 0 1 2 3 4
© Glencoe/McGraw-Hill 343 Glencoe Algebra 1
Lesson 6-1